So I have found out a little bit ago about beaver being hunted with dogs the dog main job is to find the beaver den's by working along the waters edge and picking up the scent from the air holes and setting and moving their head which way it is and then being the beaver out of the water after the shot the tracking part sounds to me like how the cops use a dog to search for drugs and I know Labs are one of the most popular ones that the cops use so what do you guys think does it sound like something a lab could be ok with

In MO it's illegal to shot a beaver or Otter in the water. Plus a decent trapper would be way more productive than a dog for beaver. Beaver dens are pretty easy to find without a dog as well. I sure wouldn't buy a dog specifically for finding beaver.